SOLUTION: Please could someone help with this question. I can't get the last part. Find real numbers a and b with a>0 such that: (a+ib)^2 = 1-1.875i So far I have got this far. a^2

Question 981120: Please could someone help with this question. I can't get the last part.
Find real numbers a and b with a>0 such that:
(a+ib)^2 = 1-1.875i
So far I have got this far.
a^2-b^2 +2abi = 1-1.875i
Real: a^2-b^2=1 (1)
Imaginary: 2ab = -1.875 (2)
Divide imaginary part (2) becomes: a =-0.9375/b (3)
I got 0.9375 =15/16
Sub in (1) gives:
(15/16)^2-b^4=b^2
b^4+b^2-225/256=0
From here I can not seem to factorize. Also I tried to use the quadratic formula but that didn't seem to work either.
Thank you in advance.
The answer given in the textbook is: a=5/4 and b=-3/4

Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!

Corresponding positions of the terms

Use the second equation and substitute for b in the first equation.

Things from this quadratic-form equation in "a" are not very neat.
Some simplification after using formula for the general solution for quadratic equation gives , not yet a to first power, so not done yet..., but at least you are finding a real number for a.

---
Further computing for a^2 finally showed (with handheld calculator help),

and since you're interested in positive values, find
.
RELATED QUESTIONS
Find real numbers a and b such that: a+ib=4 (i as in... (answered by Jk22)

This is my last question that I just do not understand if someone could help me please.... (answered by jim_thompson5910)

Find the real numbers (a) and (b) that satisfy this equation. (2+i)(a+ib)=11-2i I... (answered by ewatrrr)

This is the last question for an assignment. My mind is mush at this time, can someone... (answered by jim_thompson5910)

Hello, Need help finishing my assignment. i am stuck on a domain question? Find the... (answered by jim_thompson5910)

Can someone help me with this? Simplify the product (4 + i) (6 + 7i). Express the... (answered by jim_thompson5910)

I did the first part of this problem and it took me 3 days. I am now stuck on this second (answered by MathTherapy)

Hello, I sent in this question yesterday and I did not get a response, please someone... (answered by stanbon)

Actually some of my problems involve graphs, but maybe I can still get help on a couple... (answered by jim_thompson5910)